function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%% run the feed-forward pass
% m x 401
a1 = [ones(m, 1) X];

% m x hidden_layer_size = m x 401 x 401 x 25
z2 = a1 * Theta1';
% m x 26
a2 = [ones(m, 1) sigmoid(z2)];

% m x num_labels = m x 26 x 26 x 10
z3 = a2 * Theta2';
% a3
a3 = sigmoid(z3);

%% compute the cost
%[_, pred] = max(H, [], 2);
% mean(double(pred == y))

Y = zeros(m, num_labels);
for i = 1:m,
    Y(i,y(i)) = 1;
end;

% m x 1
J = sum(sum(-Y.*log(a3) - (1-Y).*log(1-a3) , 2)) / m;
% for i = 1:m,
%     J += sum(-1*Y(i,:).*log(a3(i,:)) - (1-Y(i,:)).*log(1-a3(i,:)));
% end;
% J = J/m;

%% add regularrization term to cost
reg = lambda*(sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2))) /2/m;

J = J + reg;
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% perform backpropagation
Delta1 = zeros(size(Theta1));
Delta2 = zeros(size(Theta2));

for t = 1:m
a1t = a1(t,:); % 1,401
z2t = z2(t,:); % 1,25
a2t = a2(t,:); % 1,26
% z3t = z3(t,:); % 1,10
a3t = a3(t,:); % 1,10
yt = Y(t,:); % 1,10

delta3 = a3t - yt; % 1,10
% sigmoidGradient是针对z2进行操作的，不包括l2的bias unit
delta2 = (delta3 * Theta2)(:,2:end) .* sigmoidGradient(z2t); % 1,26

Delta1 += delta2' * a1t; % 25,401
Delta2 += delta3' * a2t; % 10,26
end;

Theta1_grad = Delta1 ./ m;
Theta2_grad = Delta2 ./ m;

% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%

Theta2_grad(:,2:end)=Theta2_grad(:,2:end).+lambda*Theta2(:,2:end)/m;
Theta1_grad(:,2:end)=Theta1_grad(:,2:end).+lambda*Theta1(:,2:end)/m;

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
